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Loan Amortization Calculator
In short: loan amortization is the scheduled repayment of a loan, each payment covering the period’s interest and reducing the principal until the debt is gone. This calculator builds the full schedule, reports the payment and total interest, and supports both the fixed-payment French / Price method and the constant-amortization SAC method (common in Brazil).
The loan payment formula
Fixed payment: M = P × [ r(1+r)n ] ÷ [ (1+r)n − 1 ], where P = principal, r = periodic rate (annual ÷ 12), n = number of payments. SAC keeps the principal portion (P ÷ n) constant instead.
A loan amortization calculator turns a loan into a clear, period-by-period plan: how much you pay each month, how much of that payment is interest and how much reduces the debt, how the balance falls over time, and what the loan costs in total. Amortization is simply the orderly repayment of a loan through scheduled payments that cover the interest due and chip away at the principal until, by the final payment, the debt is gone.
This calculator builds the full schedule for you and reports the payment, the total interest, and the total paid, and it supports the two amortization systems used around the world: the fixed-payment French or Price method, standard in the United States, Mexico, and most of the world, and the constant-amortization SAC method, widely used in Brazil for mortgages and long-term financing, in which the payment starts higher and declines.
Whether you are sizing a mortgage, comparing auto loans, or planning business financing, seeing the whole schedule, not just the monthly payment, is what reveals the true cost of borrowing and lets you compare options on equal terms.
What amortization means
To amortize a loan is to pay it off gradually through a series of regular payments, each of which does two jobs at once: it pays the interest that has accrued on the outstanding balance since the last payment, and it repays a portion of the principal, the amount originally borrowed. Because each payment reduces the principal, the interest charged in the next period, computed on the now-smaller balance, is a little less, and so the composition of the payment shifts over time.
The essential property of an amortized loan is that this process is designed to reach exactly zero at the end of the term: the final scheduled payment clears the last of the principal along with the last of the interest, leaving nothing owed. This is what distinguishes an amortized loan from, say, an interest-only loan, where the principal is not reduced by the regular payments.
Understanding amortization is understanding this steady conversion of a lump-sum debt into a stream of payments that retire it completely.
The payment formula
For the fixed-payment method, the periodic payment is given by a standard formula: the payment equals the principal multiplied by r(1+r)^n, divided by (1+r)^n minus one, where r is the periodic interest rate and n is the number of payments. The periodic rate is the annual rate divided by the number of payments per year, so for monthly payments it is the annual rate divided by twelve.
This formula produces the single level payment that, applied every period, will exactly retire the loan by the end of the term. Take a 100,000 loan at 12 percent annual interest over one year of monthly payments: the monthly rate is one percent, n is twelve, and the payment works out to about 8,884.88. The first month interest is one percent of 100,000, or 1,000, so 7,884.88 of that first payment reduces the principal; the next month interest is charged on the reduced balance, and so on.
This calculator applies the formula and then walks through every period to build the complete schedule.
The French / Price method: fixed payments
The French method, known in Brazil and much of Latin America as the Price system, is the most common way to amortize a loan, and its defining feature is a constant total payment for the entire term. Every installment is the same size, which makes budgeting simple and predictable, but the split inside that payment changes steadily.
Because interest is always charged on the outstanding balance, and that balance is largest at the start, the early payments are mostly interest with only a small principal component; as the balance falls, the interest portion shrinks and the principal portion grows, until the final payments are almost entirely principal.
This front-loading of interest is not a fee or a trick, it is the direct arithmetic of charging interest on the remaining balance, but it explains why equity in a financed asset builds slowly at first and why early extra payments are so effective. This calculator shows the shifting interest-and-principal split for every period of a Price loan.
The SAC method: constant amortization
The SAC method, from the Portuguese sistema de amortização constante, is the constant-amortization system used widely in Brazil, especially for mortgages and long-term financing, and increasingly familiar across Latin America. Instead of holding the total payment constant, SAC holds the principal portion constant: the same amount of principal, the loan divided by the number of payments, is repaid every period.
The interest, still charged on the outstanding balance, falls steadily as that balance declines, so the total payment, principal plus interest, starts high and decreases over the life of the loan. The consequence is important: because SAC repays principal faster in the early periods than Price does, the balance shrinks more quickly, and less interest accrues overall. For the same amount, rate, and term, SAC therefore costs less total interest than Price, in exchange for higher payments at the beginning.
This calculator implements SAC fully, with its declining payments and constant principal, so you can weigh it against Price for your own situation.
Comparing Price and SAC
The choice between Price and SAC is a trade-off between the shape of the payments and the total cost. Price offers a flat, predictable payment that is easier to budget and lower at the start, which is why it dominates consumer lending in most of the world; its cost is more total interest, because the balance is paid down more slowly early on.
SAC offers payments that begin higher but fall over time, and it pays less total interest, because principal is retired faster from the outset; it suits borrowers who can afford the larger early payments and want to minimise total cost, which is why it is common in Brazilian mortgage finance. Neither is universally better: Price is easier on early cash flow, SAC is cheaper overall.
Running the same loan through both methods in this calculator makes the difference concrete, you can see the higher-but-falling SAC payments against the flat Price payment, and compare the two total-interest figures directly, which is the honest basis for choosing.
Reading the amortization schedule
The heart of this tool is the amortization schedule, the period-by-period table that shows, for each payment, the amount paid, how much of it is interest, how much reduces the principal, and the balance remaining afterward. Reading it reveals things a single payment figure hides. You can see exactly how the interest-and-principal mix shifts over the life of the loan, watch the balance decline toward zero, and identify how much interest you will have paid by any point in the term.
The schedule is also where the two methods reveal their character: in a Price schedule the payment column is flat while the interest and principal columns cross over midway; in a SAC schedule the principal column is flat while the payment and interest columns decline together.
This calculator renders the full schedule in a scrollable table and plots the balance as a falling curve alongside the interest-and-principal bars, so both the numbers and the shape of the loan are visible at a glance.
Five worked examples of loan amortization
Example 1: a fixed Price payment
Borrow 100,000 at 12% a year (1% a month) over 60 months. The level payment is 100,000 × 0.01 ÷ (1 − 1.01⁻⁶⁰) = 2,224.44 a month. Every payment is identical; only the split between interest and principal changes.
Example 2: the first month’s split
On that loan, month-one interest is 100,000 × 1% = 1,000, so principal repaid is 2,224.44 − 1,000 = 1,224.44. The balance falls to 98,775.56, and next month’s interest is charged on that smaller balance.
Example 3: total interest over the life
Sixty payments of 2,224.44 total 133,466, against 100,000 borrowed — about 33,466 in interest. Stretching the same loan to 120 months would lower the payment but raise total interest sharply.
Example 4: the SAC method (constant amortization)
Under SAC, principal is fixed at 100,000 ÷ 60 = 1,666.67 a month. Month one adds 1,000 interest for a 2,666.67 payment; payments then decline each month as the balance shrinks. Early payments are heavier than under Price.
Example 5: Price versus SAC total interest
SAC repays principal faster, so it pays less total interest than Price on the same loan — here roughly 30,500 versus 33,466. Price gives a smoother, lower initial payment; SAC costs less overall but starts higher.
Three expert tips for reading an amortization schedule
Watch the interest-to-principal shift
Early payments are mostly interest and late payments mostly principal. This is why paying a loan off early saves the most when done in the first years, while the interest share is still high.
Compare total cost, not just the payment
A longer term or the Price method gives a lower monthly payment but a higher total interest bill. Always compare the sum of all payments, not only the amount due each month.
Extra principal payments compound
Any amount paid above the scheduled payment reduces the balance that all future interest is charged on. Even small, regular overpayments shorten the term and cut total interest more than their size suggests.
How the inputs shape the loan
An amortized loan is driven by three inputs, and knowing how each moves the outcome helps you plan. The loan amount scales everything proportionally: double the principal and, at the same rate and term, the payment and the total interest roughly double. The interest rate affects both the payment and, more sharply, the total interest, because it applies to the balance every period and its effect compounds over the term; even a modest rate difference can mean a large difference in total interest on a long loan.
The term trades the size of the payment against the total cost: a longer term lowers each payment but raises the total interest, because the balance is carried for more periods, while a shorter term does the reverse. The method, finally, shapes the payment profile and the total interest without changing the amount borrowed.
This calculator lets you vary each input and see the payment, the total interest, the schedule, and the chart update immediately, which is the quickest way to understand the levers of any loan.
The true cost of borrowing
The single most useful habit this calculator encourages is to look past the monthly payment to the total cost. Lenders and advertisements naturally emphasise the monthly payment, because a small monthly figure sells a loan, but the monthly payment says little about what the loan actually costs; a long term produces a low payment and a high total interest, and two loans with the same payment can cost very different amounts depending on their terms and rates.
The total interest, and the total amount paid, are the honest measures of cost, and this calculator reports both prominently alongside the payment. When comparing loan offers, or deciding on a term, or weighing Price against SAC, the total-interest figure is the number to watch.
Seeing it change as you adjust the inputs, and especially seeing how much a longer term or a higher rate adds to it, is the clearest antidote to being sold on a low monthly payment that hides a high lifetime cost.
Where loan amortization fits in the industrial-finance toolkit
Loan amortization connects to the rest of this silo through the cost and structure of debt. The interest rate on a loan is a direct input to the cost of debt, which, after the tax shield, is one of the two components of the weighted average cost of capital that the WACC calculator computes; the WACC in turn draws its cost of equity from the CAPM calculator.
The amount and terms of a company borrowing shape its capital structure, which affects the WACC and, through it, the value-creation measures, the ROIC-versus-WACC spread in the ROI calculator and the economic value added in the EVA calculator. And the schedule this tool produces, with its split of payments into interest and principal, feeds the liquidity and leverage analysis of the financial-ratios calculator.
Read together, the tools trace debt from its terms and repayment schedule here, through its cost in the WACC, to its effect on value and financial health across the silo. Because they share consistent conventions, figures move cleanly between them, letting you build a coherent picture of how financing decisions ripple through a business.
Practical tips for using the schedule
A few habits make the amortization schedule more useful in practice. First, compare loans on total interest and total paid, not on the monthly payment alone, so that a tempting low payment on a long term does not disguise a high lifetime cost. Second, when you can afford it, consider the effect of paying a little extra toward principal early: because interest is charged on the balance, early principal reductions save interest for every remaining period, and the schedule makes clear how front-loaded the interest is.
Third, if minimising total interest matters more than a flat payment, look at the SAC method, whose faster early principal repayment lowers the total cost. Fourth, match the rate you enter to the loan actual nominal annual rate and confirm the term, since small input errors change the result. And finally, use the schedule to plan ahead: knowing the remaining balance at any point tells you what it would take to settle the loan early or how much equity you have built.
This calculator supports all of these uses by making the full schedule and the totals visible and instantly recalculated.
Nominal rate, effective rate, and the true cost
One subtlety worth understanding is the difference between the nominal annual rate you enter and the effective rate you actually pay. This calculator, like most, converts a nominal annual rate to a periodic rate by simple division, the annual rate divided by twelve for monthly payments, which is the market convention for quoting loans. But because interest compounds each period, the effective annual rate, the rate that reflects that compounding, is slightly higher than the nominal rate: a 12 percent nominal rate compounded monthly works out to an effective annual rate of about 12.68 percent.
For comparing loans, what matters most is consistency, comparing like with like, and looking at the total interest the schedule produces, which already embeds the compounding. Many jurisdictions also require lenders to quote an annual percentage rate, or APR, that folds certain fees into the rate to give a fuller picture of cost; the APR can therefore exceed the quoted interest rate.
When you use this calculator, enter the nominal rate the lender quotes, read the total interest for the true periodic cost, and remember that fees outside the interest rate, if any, would add to the real cost beyond what the schedule shows.
Fixed versus variable interest rates
This calculator assumes a fixed interest rate for the life of the loan, which is the right model for fixed-rate mortgages, most auto loans, and many business term loans, and it produces an exact schedule for them. Many loans, however, carry a variable or floating rate that resets periodically against a benchmark, so the payment or the term changes over time as rates move.
For a variable-rate loan, the schedule this calculator produces is still a useful snapshot under the current rate, showing what the payments and total interest would be if the rate held, but the actual figures will drift as the rate changes. A common way to use the tool for a variable loan is to run it at the current rate for a baseline, then re-run it at higher and lower rates to bracket the range of outcomes, which reveals how exposed the loan is to rate movements.
Fixed-rate borrowers get certainty at the cost of usually starting a little higher; variable-rate borrowers get a lower initial rate at the cost of uncertainty. Seeing the schedule at several rates makes that trade-off tangible.
Amortization in business and project finance
Amortization is not only a consumer concept; it is central to how businesses structure debt and how projects are financed. A company that borrows to fund equipment, expansion, or an acquisition typically repays through an amortizing term loan, and the schedule determines the cash outflow it must cover each period, which feeds directly into cash-flow planning and the coverage ratios lenders scrutinise.
The choice between a Price-style level payment and a SAC-style declining payment matters here too: level payments are easier to match against steady operating cash flow, while declining payments suit projects whose cash generation is strongest early. In project finance, the amortization profile is often sculpted to match the project expected cash flows, so that debt service never outruns the cash available to pay it. The interest portion of each payment is also tax-relevant, since interest is usually deductible, which is the same tax shield that lowers the after-tax cost of debt in the WACC.
Used at the business level, this calculator helps translate a financing decision into the concrete schedule of payments that a company must plan around, and links directly to the cost-of-capital and value tools elsewhere in this silo.
Amortized loans versus interest-only and balloon loans
The amortized loan this calculator models, one that is fully paid off by regular payments over its term, is the most common structure, but it is not the only one, and knowing the alternatives clarifies what amortization actually buys you.
An interest-only loan requires payments that cover only the interest, leaving the principal untouched, so the balance never falls and the full principal is due as a lump sum at the end; the payments are lower, but no equity is built and the debt is not retired by the regular payments.
A balloon loan is a hybrid: it amortizes on a long schedule for a while, producing modest payments, but the full remaining balance falls due as a large balloon payment before the loan would naturally end, so the borrower must refinance or repay the lump sum. Both structures lower the periodic payment at the cost of leaving principal outstanding, which means more total interest and a large obligation later.
The fully amortized loan, by contrast, retires the debt steadily and predictably, which is why it is the default for most borrowers and the structure this calculator schedules. Understanding the contrast helps you recognise when a low payment is low because the loan is amortizing slowly or not at all, a crucial thing to see before signing.
The power of prepayment, illustrated
Because the front-loading of interest in a Price loan is so pronounced, prepayment, paying more than the required amount toward principal, is one of the most effective ways a borrower can save money, and the schedule makes it easy to see why. Every extra unit of principal you repay is a unit that will never accrue interest again for the rest of the term, so the saving is the interest that principal would have generated over all the remaining periods.
Early in the loan, when the balance is large and the remaining term is long, that saving is greatest; the same extra payment made near the end saves very little, because little interest remains to be charged. This is why a lump sum applied in year one of a long mortgage can save far more than the same sum applied in year fifteen, and why even small, regular extra payments compound into meaningful savings and a shorter term. The mechanism is identical to what makes SAC cheaper than Price: both retire principal faster and so starve future interest.
While this calculator computes the contractual schedule, reading how much of each early payment is interest shows you exactly how much room prepayment has to work, and it is often more than borrowers expect.
Common mistakes to avoid
A few recurring errors trip people up with amortization, and avoiding them keeps the schedule honest. The first is judging a loan by its monthly payment alone: a low payment can simply mean a long term and a high total interest, so always read the total-interest figure the calculator reports.
The second is confusing the nominal rate with the effective rate or the all-in cost, forgetting that compounding and any fees make the true cost higher than the quoted rate. The third is mismatching the rate and the payment frequency, for example entering an annual rate while expecting a monthly schedule without conversion; this calculator handles the monthly conversion for you, but the rate you enter must be the nominal annual rate.
The fourth is assuming a fixed-rate schedule describes a variable-rate loan exactly, when in reality the payments will drift as the benchmark moves. The fifth is overlooking the method: comparing a Price payment against a SAC first payment without noting that SAC payments fall over time and usually cost less interest overall.
And the sixth is ignoring prepayment potential, treating the contractual schedule as fixed when extra principal payments can meaningfully shorten the loan and cut its cost. The calculator does the arithmetic exactly; these judgments about how to read and compare loans are what turn an accurate schedule into a good decision.
A final habit worth building is to keep the three drivers, amount, rate, and term, in view together rather than optimising one in isolation.
Borrowers often fixate on securing the lowest rate, which matters, but a longer term at a low rate can still cost more in total interest than a shorter term at a slightly higher one, and the reverse can also be true; only the total-interest figure settles it.
Run the realistic combinations through the calculator, read the total interest for each, and let that number, alongside the payment you can comfortably sustain, guide the choice. That simple discipline, comparing total cost rather than any single input, is what separates a loan that merely looks affordable from one that genuinely is.
Frequently asked questions
What is loan amortization?
Loan amortization is the process of paying off a loan over time through regular, scheduled payments, each of which covers the interest due for the period and reduces the outstanding principal. An amortization schedule lays out every payment across the life of the loan, showing how much of each goes to interest, how much to principal, and what balance remains afterward.
The defining feature of an amortized loan is that it is fully paid off, principal and interest, by the final scheduled payment, with nothing left owing. Most consumer and business loans, mortgages, auto loans, personal loans, and many commercial loans, are amortized this way.
This calculator builds the full schedule for you and reports the payment, the total interest over the life of the loan, and the total amount paid, using either the fixed-payment (French / Price) method or the constant-amortization (SAC) method.
What is the loan payment formula?
For a fixed-payment amortized loan, the periodic payment is M = P × [ r(1+r)^n ] ÷ [ (1+r)^n − 1 ], where P is the principal, r is the periodic interest rate (the annual rate divided by the number of payments per year), and n is the total number of payments. The payment is the same every period; what changes is its split between interest and principal.
For example, a 100,000 loan at 12 percent annual interest over 12 monthly payments has a monthly rate of one percent and a payment of about 8,884.88, of which the first month is 1,000 interest (one percent of 100,000) and the rest principal.
This calculator applies this formula for the Price method, and for the SAC method it instead keeps the principal portion constant and lets the payment decline; in both cases it shows the full period-by-period breakdown.
What is the difference between the Price and SAC methods?
The two most common amortization systems differ in what they hold constant. The French or Price method keeps the total payment constant for the whole term: every installment is identical, but because interest is charged on a shrinking balance, the interest portion falls over time and the principal portion rises to compensate.
The SAC method, the constant-amortization system widely used in Brazil for mortgages and long-term financing, instead keeps the principal portion constant, so the same amount of principal is repaid each period while the interest, charged on a falling balance, declines; the result is a payment that starts high and decreases steadily.
For the same loan amount, rate, and term, SAC pays down the balance faster in the early periods, so it incurs less total interest than Price, at the cost of higher payments at the start. This calculator offers both methods so you can compare them directly.
Why is so much of my early payment interest?
In a fixed-payment (Price) loan, the interest each period is charged on the outstanding balance, which is at its largest at the beginning, so the early payments are dominated by interest and contribute relatively little to principal. As the balance falls, the interest portion shrinks and a larger share of each identical payment goes to principal, until near the end almost all of it reduces the balance.
This front-loading of interest is a natural consequence of charging interest on the remaining balance, not a hidden fee, but it has a practical implication: in the early years you build equity slowly, and paying a little extra toward principal early can save a disproportionate amount of interest over the life of the loan. The SAC method reduces this effect by repaying a constant amount of principal from the very first payment.
This calculator shows the interest and principal split for every period so the pattern is fully visible.
How is total interest calculated?
The total interest over the life of a loan is simply the sum of the interest portions of every payment, which also equals the total amount paid minus the original principal. For a fixed-payment loan, total paid is the level payment multiplied by the number of payments, so total interest is that figure minus the principal. The total interest depends on three things: the amount borrowed, the interest rate, and the term.
A longer term lowers each payment but increases total interest, because the balance is carried for longer; a higher rate raises both the payment and the total interest. This is why extending a loan to reduce the monthly payment can be costly overall, and why comparing loans on total interest, not just the monthly payment, matters.
This calculator reports the total interest and the total paid alongside the payment, so you can see the full cost, not only the monthly figure.
Does a longer term reduce the total cost of a loan?
No, quite the opposite. A longer term reduces the size of each payment, which can make a loan more affordable month to month, but it increases the total interest paid, because the principal is outstanding for longer and interest accrues on it for more periods. For example, stretching a loan from ten years to twenty roughly halves the payment but can more than double the total interest, depending on the rate.
The right term is a trade-off between the monthly payment you can comfortably afford and the total cost you are willing to bear over the life of the loan. This calculator makes the trade-off concrete: change the term and watch the payment fall while the total interest rises.
Comparing the total-interest figure across different terms, rather than fixating on the monthly payment, is the key to seeing the true cost of borrowing.
Can I use this for a mortgage, auto loan, or personal loan?
Yes. The amortization mathematics is the same for any fully amortized loan, so this calculator works for mortgages, auto loans, personal loans, student loans, and most business term loans. Enter the amount borrowed, the annual interest rate, and the term, and choose the method; the calculator produces the payment and the full schedule regardless of the loan type.
The main things to check are that the rate you enter is the nominal annual rate and that the term matches the payment frequency the calculator assumes, which is monthly. For loans with features such as balloon payments, variable rates, or fees rolled into the balance, the basic schedule still gives a close and useful picture, though those extra features would need separate treatment.
For the common case of a straightforward fixed-rate amortized loan, this calculator gives an exact schedule.
What is the remaining balance and why does it matter?
The remaining balance, or outstanding principal, is the amount still owed on the loan after any given payment, and it is the figure interest is charged on for the next period. The amortization schedule shows this balance falling after every payment until it reaches zero at the end of the term.
The remaining balance matters for several practical reasons: it is what you would need to pay to settle the loan early, it determines how much equity you have built in a financed asset, and it is the base for calculating each period interest. Because interest is always charged on the current balance, paying down the balance faster, through extra payments or a method like SAC, directly reduces future interest.
This calculator displays the remaining balance for every period in the schedule and plots it as a declining curve, so you can see exactly how the debt is retired over time.
Does paying extra toward principal help?
Yes, and often substantially, especially early in a fixed-payment loan. Any extra amount paid toward principal reduces the outstanding balance immediately, and because all future interest is charged on that balance, every period thereafter accrues less interest, so a single extra payment early on can save many times its size in interest over the remaining life of the loan.
The earlier the extra payment, the greater the saving, because it removes principal that would otherwise have accrued interest for the longest time. This is the same reason the SAC method, which front-loads principal repayment, costs less total interest than Price. While this calculator computes the standard schedule for a set payment, understanding this principle helps you see why prepayment is powerful: it attacks the balance that drives all future interest.
Even modest extra principal payments, made consistently and early, can shorten a loan and cut its total cost meaningfully.
Does this calculator store the numbers I enter?
No. The calculator runs entirely in your browser. The loan amount, interest rate, and term you enter are never sent to our servers, stored, or shared. You can use it freely for confidential figures. See our Privacy Policy for details.
Is the loan amortization calculator free to use?
Yes. This calculator, like every tool on OpsCalculators, is free and needs no account or sign up. There is no paywall and no limit on how many calculations you can run, and you can switch between the Price and SAC methods and change the inputs as often as you like.
How does the interest rate affect the schedule?
The interest rate is one of the three drivers of an amortized loan, alongside the amount and the term, and it affects both the payment and the total interest. A higher rate raises the interest charged on the balance each period, which raises the fixed payment (in the Price method) and increases the total interest paid over the life of the loan; a lower rate does the reverse.
The rate also shapes the interest-versus-principal split: at higher rates, a larger share of early payments goes to interest, so the balance falls more slowly at first. Because the effect compounds over many periods, even a small difference in rate can translate into a large difference in total interest on a long loan, which is why shopping for a lower rate is worthwhile.
This calculator recomputes the entire schedule instantly when you change the rate, so you can see how sensitive the payment and total cost are to it.
Related industrial finance calculators
More tools in this silo. Return to the Industrial Finance hub for the full set.
Sources, disclaimer and editorial transparency
Method follows the standard treatment of loan amortization in corporate finance, including the fixed-payment (French / Price) and constant-amortization (SAC) systems as documented by financial institutions and the texts by Brealey, Myers and Allen. See our Editorial Policy for how we research and review each tool.
This calculator is for education and planning and does not constitute financial, tax, or investment advice. Confirm any figure that informs a real decision with a qualified professional. OpsCalculators is operated by MAFHH INTERNATIONAL LTD; see our Privacy Policy.